CN103117969A - Multi-modulus blind equalization method using wavelet frequency domain transform based on fractional lower order statistics - Google Patents

Abstract

The invention provides a multi-modulus blind equalization method using wavelet frequency domain transform based on fractional lower order statistics. The method includes stabilizing distributed noise by fractional lower order statistics inhibition alpha, transforming multiple amplitude moduli into a single amplitude modulus by modulus transform, and introducing orthogonal wavelet transform and fast Fourier transform to multi-modulus blind equalization. Effective equalization of MQAM (M-order quadrature amplitude modulation) signals is achieved by modulus transform, statistics is reduced by means of FFT (fast Fourier transform) and over-lapping reservation, the signals are subjected to orthogonal wavelet transform before entering a balancer, and accordingly autocorrelation of input signals is reduced. The method has high convergence rate and small steady-state errors and is of certain application value in the field of underwater acoustic communication.

Description

A kind of fractional lower-order statistics mould value transform wavelet frequency domain multimode blind balance method

Technical field

The invention belongs to underwater sound wireless communication technology field, specifically refer to a kind of fractional lower-order statistics mould value transform wavelet frequency domain multimode blind balance method.

Background technology

In underwater sound communication system, by the intersymbol interference (inter-symbol interference, ISI) that multipath effect and channel distortions cause, reduced transmission rate and the reliability of information.In order to overcome the ISI in underwater acoustic channel, need to adopt the blind adaptive balancing technique to eliminate.The blind adaptive balancing technique does not become the focus of underwater sound communication area research because it does not need the transmitting training sequence, time domain constant modeling method (constant modulus algorithm, CMA) be most widely used, the method is highly suitable for the equilibrium to the norm signal.Yet the constellation of non-norm M rank quadrature amplitude modulation signals (MQAM) and its statistics mould value are not mated, and cause CMA relatively poor to the portfolio effect of MQAM (for example 16QAM signal).After by the mould value transform, a plurality of amplitude mould value transforms of non-norm MQAM being become single amplitude mould value, it is carried out equilibrium, effectively reduce steady-state error.

In traditional blind adaptive equalization methods (abbreviation blind balance method), interchannel noise all is assumed to be Gaussian noise, but studies show that in a large number in recent years, some noises in actual channel often show as stronger pulse feature, and incomplete Gaussian distributed model, but a kind of stable Generalized Gaussian Distribution Model that distributes of α that is called.Stablize in partition noise at α, the second-order statistic of signal is non-existent, and is no longer applicable based on the signal processing method of signal second-order statistic, therefore needs to adopt fractional lower-order statistics that signal is analyzed and processed.

Frequency domain constant modeling method (frequency domain constant modulus algorithm, FCMA) traditional time domain blind balance method is transformed to frequency domain and carry out Blind equalization processing, owing to having utilized fast Fourier transform (fast fourier transform, FFT) and overlap-save method (overlap-save law, OSL), reduced the amount of calculation of time domain blind balance method.Orthogonal wavelet transformation is incorporated in blind balance method, utilizes the orthogonal wavelet decorrelation good to equalizer input signal, accelerated convergence rate.

In sum, in prior art, α is stablized under the partition noise channel condition, multimode blind equalization problem does not also form complete, an effective technical scheme.

Summary of the invention

Technical problem to be solved by this invention is to overcome the deficiencies in the prior art, stablize that the partition noise performance is degenerated and shortcoming that can't efficient balance 16 rank quadrature amplitude modulation multimode signals for time domain constant modeling method CMA at α, propose a kind of fractional lower-order statistics mould value transform wavelet frequency domain multimode blind balance method WT-FLOSMTFMMA; Described method is utilized fractional lower-order statistics to stablize partition noise to α to suppress, utilize the mould value transform that a plurality of amplitude mould value transforms are become single amplitude mould value, to reduce steady-state error; Utilize fast Fourier transform and overlap-save method, to reduce the amount of calculation of traditional blind balance method; Utilize orthogonal wavelet transformation, to reduce the autocorrelation of equalizer input signal.

In order to solve the problems of the technologies described above, the technical solution adopted in the present invention is:

A kind of fractional lower-order statistics mould value transform wavelet frequency domain multimode blind balance method comprises the steps:

Steps A, a (n) that will transmit obtains channel output vector b (n) through impulse response channel c (n), and wherein n is time series;

Step B adopts α to stablize partition noise w (n) and the described channel output vector of steps A b (n) obtains the front equalizer input signal y (n) of orthogonal wavelet transformation: y (n)=w (n)+b (n);

Step C gets its real part y to the described equalizer input signal y of step B (n) _r(n) and imaginary part y _i(n), then to real part y _r(n) and imaginary part y _i(n) carry out respectively orthogonal wavelet transformation, through the signal after orthogonal wavelet transformation be

v _r(n)=Qy _r(n)，v _i(n)=Qy _i(n)

In formula, Q is the orthogonal wavelet transformation matrix, v _r(n) and v _i(n) be respectively the real part y of time-domain equalizer input signal y (n) _r(n) and imaginary part y _i(n) through the signal component after orthogonal wavelet transformation, the real part Z of frequency-domain equalizer output Z (N) _r(N) and imaginary part Z _i(N) be respectively

Z _r(N)=R _r(N)F _r(N)，Z _i(N)=R _i(N)F _i(N)

In formula, N represents that length is the piece number of the data block of L, and L is equalizer weight vector length, F _r(N) and F _i(N) be respectively real part and the imaginary part of frequency-domain equalizer weight vector F (N), R _r(N) and R _i(N) be respectively v _r(n) and v _i(n) through frequency domain real part and imaginary part after fast Fourier transform;

Step D is to the real part Z of step C frequency-domain equalizer output signal Z (N) _r(N) and imaginary part Z _i(N) obtain respectively the real part z of time-domain equalizer output signal z (n) as Fourier inversion _r(n) and imaginary part z _i(n).

In described step C, the calculation procedure of frequency-domain equalizer weight vector F (N) is as follows:

Step C-1 calculates mould value transform time domain error function e _t(n) real part e _rt(n) with imaginary part e _it(n), computing formula is as follows:

$e_{\mathrm{rt}}\left(n\right)=R_{\mathrm{rt}}^{\left(p\right)}-{\left|z_{\mathrm{rt}}\left(n\right)\right|}^p,$ $e_{\mathrm{it}}\left(n\right)=R_{\mathrm{it}}^{\left(p\right)}-{\left|z_{\mathrm{it}}\left(n\right)\right|}^p$

$R_{\mathrm{rt}}^{\left(p\right)}=\frac{E\left\{{\left|a_{\mathrm{rt}}\left(n\right)\right|}^{2p}\right\}}{E\left\{{\left|a_{\mathrm{rt}}\left(n\right)\right|}^p\right\}},$ $R_{\mathrm{it}}^{\left(p\right)}=\frac{E\left\{{\left|a_{\mathrm{it}}\left(n\right)\right|}^{2p}\right\}}{E\left\{{\left|a_{\mathrm{it}}\left(n\right)\right|}^p\right\}}$

In formula, || be modulo operation, p be greater than zero less than 1 positive number, E{} represents to ask mathematic expectaion, a _rt(n) and a _it(n) be respectively the real part a of a that transmits (n) _r(n) with imaginary part a _i(n) pass through respectively signal component after the mould value transform,

With

Be respectively a _rt(n) and a _it(n) p rank statistics mould value, z _rt(n) and z _it(n) be respectively the real part z of time-domain equalizer output signal z (n) _r(n) with imaginary part z _i(n) through real part and imaginary part after the mould value transform; Step C-2 is to mould value transform time domain error function e _t(n) real part e _rt(n) with imaginary part e _it(n) make Fourier transform after, obtain mould value transform error of frequency domain function E _t(N) real part E _rt(N) with imaginary part E _it(N);

Step C-3 calculates frequency-domain equalizer weight vector F (N), and the formula of its iterative process is:

$F_r(N+1)=F_r\left(N\right)+\mathrm{\μ}{\hat{R}}^{-1}\left(N\right)\left|E_{\mathrm{rt}}\left(N\right)\right|$

$\·\mathrm{sign}\left(E_{\mathrm{rt}}\left(N\right)\right){\left|Z_{\mathrm{rt}}\left(N\right)\right|}^{p-1}\mathrm{sign}\left(Z_{\mathrm{rt}}\left(N\right)\right)R_r^{*}\left(N\right)$

$F_i(N+1)=F_i\left(N\right)+\mathrm{\μ}{\hat{R}}^{-1}\left(N\right)\left|E_{\mathrm{it}}\left(N\right)\right|$

$\·\mathrm{sign}\left(E_{\mathrm{it}}\left(N\right)\right)|Z_{\mathrm{it}}\left(N\right){|}^{p-1}\mathrm{sign}\left(Z_{\mathrm{it}}\left(N\right)\right)R_i^{*}\left(N\right)$

In formula, μ is iteration step length, and symbolic operation, Z are got in sign () expression _rt(N) and Z _it(N) be respectively through the frequency-domain equalizer output signal Z after the mould value transform _t(N) real part and imaginary part;

With

The real part R of expression frequency-domain equalizer input signal R (N) _r(N) with imaginary part R _i(N) conjugation;

For

Fast Fourier transform, and

The formula that obtains be:

${\hat{R}}^{-1}\left(n\right)=\mathrm{diag}[{\mathrm{\σ}}_{j,0}^2\left(n\right),{\mathrm{\σ}}_{j,1}^2\left(n\right),\·\·\·,{\mathrm{\σ}}_{j,k}^2\left(n\right),{\mathrm{\σ}}_{J+\mathrm{1,0}}^2\left(n\right),\·\·\·,{\mathrm{\σ}}_{J+1,k_J-1}^2\left(n\right)]$

Wherein, diag[] the expression diagonal matrix,

With

Represent u respectively _{J, k}(n) with

Average power estimate, can be obtained by the following formula recursion:

${\mathrm{\σ}}_{j,m}^2(n+1)={\mathrm{\β}}_{\mathrm{\σ}}{\mathrm{\σ}}_{j,m}^2\left(n\right)+(1-{\mathrm{\β}}_{\mathrm{\σ}}){\left|u_{j,m}\left(n\right)\right|}^2$

${\mathrm{\σ}}_{J+1,m}^2(n+1)={\mathrm{\β}}_{\mathrm{\σ}}{\mathrm{\σ}}_{J+1,m}^2\left(n\right)+(1-{\mathrm{\β}}_{\mathrm{\σ}}){\left|s_{J,m}\left(n\right)\right|}^2$

In formula, u _{J, m}(n) be that scale parameter is that j, translation parameters are the wavelet conversion coefficient of m, s _{J, m}(n) for scale parameter is that J, translation parameters are the change of scale coefficient of m, J is the out to out of wavelet decomposition, and k is the translation parameters of corresponding wavelet function under scale parameter j, k _JThe expression out to out is the maximal translation of wavelet function under J, β _σSmoothing factor, and 0＜β _σ＜1.

The invention has the beneficial effects as follows: the present invention proposes a kind of fractional lower-order statistics mould value transform wavelet frequency domain multimode blind balance method, when described method utilizes fractional lower-order statistics inhibition α to stablize partition noise, utilize the mould value transform that a plurality of amplitude mould value transforms are become single amplitude mould value, then orthogonal wavelet transformation, fast Fourier transform are incorporated in the multimode blind balance method.Described method has realized efficient balance to M rank quadrature amplitude modulation signal MQAM by the mould value transform, utilize simultaneously FFT and overlap-save method to reduce amount of calculation, and before signal enters equalizer, it is carried out orthogonal wavelet transformation, reduced the autocorrelation of input signal.The inventive method has convergence rate and less steady-state error faster, has certain using value in the underwater sound communication field.

Description of drawings

Fig. 1: be the inventive method WT-FLOSMTFMMA schematic diagram.

Fig. 2: be 16QAM signal constellation (in digital modulation) figure.

Fig. 3: be the MTMMA schematic diagram.

Fig. 4: be the FCMA schematic diagram.

Fig. 5: be the MTFMMA schematic diagram.

Fig. 6: be the FLOSMTFMMA schematic diagram.

Fig. 7: embodiment is figure as a result, the mean square error curve of 3 kinds of methods of Fig. 7 (a), and 7 (b) FLOSFCMA exports planisphere, and 7 (c) FLOSMTFMMA exports planisphere, and 7 (d) WT-FLOSMTFMMA exports planisphere.

Fig. 8: be the embodiment figure as a result in different error of frequency domain function index situations, the mean square error curve of 8 (a) 3 kinds of methods, 8 (b) FLOSFCMA exports planisphere, and 8 (c) FLOSMTFMMA exports planisphere, and 8 (d) WT-FLOSMTFMMA exports planisphere.

Embodiment

Below in conjunction with accompanying drawing, a kind of fractional lower-order statistics mould value transform wavelet frequency domain multimode blind balance method that the present invention is proposed is elaborated:

A. mould value transform method

The amplitude mould value of M rank quadrature amplitude modulation signals (MQAM) a (n) | a (n) | not constant, be not equal to its second-order statistics mould value R yet ²=E{|a (n) | } ⁴/ E{|a (n) | } ²Square root; The real part a of a (n) _r(n) mould value | a _r(n) | also be not equal to a _r(n) second-order statistics mould value

Square root, the imaginary part a of a (n) _i(n) mould value | a _i(n) | also be not equal to a _i(n) second-order statistics mould value

Square root; || be modulo operation, E{} represents to ask mathematic expectaion.The now explanation as an example of the 16QAM signal example can make the amplitude mould value of 16QAM signal a (n) equate with its statistics mould value by mould value transform method.

Fig. 2 has provided 16QAM signal constellation (in digital modulation) figure, and as seen from Figure 2, the 16QAM signal is non-norm complex signal a (n), and therefore real part and the imaginary component with this signal drives the row consideration into.In the 16QAM planisphere, the real part a of a (n) signal _r(n) with imaginary part a _i(n) corresponding amplitude mould value is respectively | a _r(n) |=1 or 3, | a _i(n) |=1 or 3; The real part a of a (n) _r(n) with imaginary part a _i(n) statistics mould value is respectively

(

The expression extracting operation), at this moment

Therefore, the CMA method can not be carried out efficient balance to the 16QAM signal.The mould value transform equation that will transmit is defined as

|a _rt(n)|=||a _r(n)|-2|,|a _it(n)|=||a _i(n)|2| (1)

In formula, | a _rt(n) | and | a _it(n) | be respectively a that transmits after the mould value transform _t(n) real part a _rt(n) with imaginary part a _it(n) mould value, will | a _r(n) | and | a _i(n) | substitution formula (1) | a _rt(n) |=1, a _it(n) |=1, a transmits after the mould value transform _tThe statistics mould value of real part (n) and imaginary part is respectively

At this moment, the mould value that transmits after the mould value transform equates with its statistics mould value, namely $\left|a_{\mathrm{it}}\left(n\right)\right|=\sqrt{R_{\mathrm{it}}^2}=1.$

B. mould value transform time domain multimode blind balance method

After by the mould value transform, multimode 16QAM signal being become single mould value, just can be by the CMA method to its efficient balance.Thisly by the mould value transform, the blind balance method that multimode signal becomes single mode signal is called mould value transform time domain multimode blind balance method (MTMMA), as shown in Figure 3.The cost function of the method is defined as

$J_{\mathrm{MTMMA}}=E\{{[R_{\mathrm{rt}}^2-|z_{\mathrm{rt}}\left(n\right){|}^2]}^2+[R_{\mathrm{it}}^2-\left|z_{\mathrm{it}}\left(n\right){|}^2{]}^2\right\}---\left(2\right)$

In formula, J _MTMMACost function for MTMMA; | z _rt(n) |=|| z _r(n) |-2|, | z _it(n) |=|| z _i(n) |-2| is respectively mould value transform equalizer output signal z _t(n) real part z _rt(n) with imaginary part z _it(n) mould value; z _r(n) and z _i(n) be respectively real part and the imaginary part of time-domain equalizer output signal z (n).

The weight vector iterative formula of MTMMA is

$f_r(n+1)=f_r\left(n\right)+\mathrm{\μ}\left|z_{\mathrm{rt}}\left(n\right)\right|[1-|z_{\mathrm{rt}}\left(n\right){|}^2\left]\mathrm{sign}\right[z_r\left(n\right)]y_r^{*}\left(n\right)$ (3)

$f_i(n+1)=f_i\left(n\right)+\mathrm{\μ}\left|z_{\mathrm{it}}\left(n\right)\right|[1-|z_{\mathrm{it}}\left(n\right){|}^2\left]\mathrm{sign}\right[z_i\left(n\right)]y_i^{*}\left(n\right)$

In formula, μ is iteration step length, and symbolic operation is got in sign () expression,

With

Be respectively the real part y of time-domain equalizer input signal y (n) _r(n) with imaginary part y _i(n) conjugation, f _r(n) and f _r(n) be respectively real part and the imaginary part of time-domain equalizer weight vector f (n).

C. frequency domain norm blind balance method

Frequency domain norm blind balance method (FCMA) principle, as shown in Figure 4.By Fig. 4, the signal before process fast Fourier transform FFT is carried out piecemeal, the length of every block signal equals equalizer weight vector length L, the every L sampling point of weight vector once upgrades, the each renewal by L error signal sampling point accumulation result controlled, this has just guaranteed with time domain blind balance method CMA, identical convergence rate is arranged, simultaneously by fast Fourier transform (FFT) and overlap-save method (OSL), utilize circular convolution to replace the linear convolution of time-domain signal, make computation amount.

The error function of FCMA is defined as

$E\left(N\right)=R_F^2-|Z\left(N\right){|}^2---\left(4\right)$

In formula, N represents that length is the piece number of the data block of L,

Second order frequency domain statistics mould value for a that transmits (n).

By the weight vector of CMA new formula more, the weight vector that gets FCMA more new formula is

F(N+1)=F(N)+μE(N)Z(N)Y ^*(N) (5)

In formula, Z (N) is the frequency-domain equalizer output signal, is the fast Fourier transform of z (n); F (N) is the frequency-domain equalizer weight vector, is the fast Fourier transform of f (n); Y ^*(N) be the conjugation of frequency-domain equalizer input signal Y (N), Y (N) is the fast Fourier transform of y (n).

D. mould value transform frequency domain multimode blind balance method

The mould value transform is incorporated in frequency domain norm blind balance method, obtains mould value transform frequency domain multimode blind balance method (MTFMMA), as shown in Figure 5.The cost function of the method is

$J_{\mathrm{MTFMMA}}=E\left\{{[R_{\mathrm{rtF}}^2-|z_{\mathrm{rt}}\left(N\right){|}^2]}^2\right\}+E\left\{\right[R_{\mathrm{itF}}^2-\left|z_{\mathrm{it}}\left(N\right){|}^2{]}^2\right\}---\left(6\right)$

In formula, J _MTFMMABe the cost function of MTFMMA, Z _rt(N) and Z _it(N) be respectively through frequency-domain equalizer output signal Z after the mould value transform _t(N) real part and imaginary part, With

Be respectively the real part a of a that transmits (n) _r(n) with imaginary part a _i(n) Fourier transform of the second-order statistics mould value after the mould value transform.The weight vector of MTFMMA more new formula is

$F_r(N+1)=F_r\left(N\right)+\mathrm{\μ}\left(\right|R_{\mathrm{rtF}}^2-Z_{\mathrm{rt}}\left(N\right){|}^2)\left|Z_{\mathrm{rt}}\left(N\right)\right|\mathrm{sign}\left[Z_r\left(N\right)\right]Y_r^{*}\left(N\right)$ (7)

$F_i(N+1)=F_i\left(N\right)+\mathrm{\μ}\left(\right||R_{\mathrm{itF}}^2-Z_{\mathrm{it}}\left(N\right){|}^2)\left|Z_{\mathrm{it}}\left(N\right)\right|\mathrm{sign}\left[Z_i\left(N\right)\right]Y_i^{*}\left(N\right)$

In formula,

With

Be respectively the real part of frequency-domain equalizer input signal Y (N) and the conjugation of imaginary part, be respectively

With

Fast Fourier transform; Z _r(N) and Z _i(N) represent respectively real part and the imaginary part of frequency-domain equalizer output Z (N), be respectively z _r(n) and z _i(n) fast Fourier transform; F _r(N) and F _i(N) be respectively real part and the imaginary part of frequency-domain equalizer weight vector F (N), be respectively f _r(n) and f _i(n) fast Fourier transform.

E. fractional lower-order statistics mould value transform frequency domain multimode blind balance method

Stablize in partition noise at α, utilize the fractional lower-order statistics of error function, will obtain fractional lower-order statistics mould value transform frequency domain multimode blind balance method (FLOSMTFMMA).The method principle, as shown in Figure 6.The cost function of the method is

J _FLOSMTFMMA=E{|E _rt(N)| ²+|E _it(N)| ²} (8)

$E_{\mathrm{rt}}\left(N\right)=R_{\mathrm{rtF}}^{\left(p\right)}-|Z_{\mathrm{rt}}\left(N\right){|}^p,$ $E_{\mathrm{it}}\left(N\right)=R_{\mathrm{itF}}^{\left(p\right)}-|Z_{\mathrm{it}}\left(N\right){|}^p---\left(9\right)$

In formula, J _FLOSMTFMMACost function for FLOSMTFMMA; P is less than 1 positive number, E greater than zero _rt(N) and E _it(N) be respectively mould value transform time domain error function e _t(n) real part e _rt(n) with imaginary part e _it(n) Fourier transform; With Be respectively the real part p rank statistics mould value of a that transmits (n)

With imaginary part p rank statistics mould value

Fast Fourier transform, lower with.By steepest descent method, the weight vector of goals for low order statistic mould value transform frequency domain multimode blind balance method (FLOSMTFMMA) more new formula is

$F_r(N+1)=F_r\left(N\right)+\mathrm{\μ}\left|E_{\mathrm{rt}}\left(N\right)\right|$

$\·\mathrm{sign}\left(E_{\mathrm{rt}}\left(N\right)\right){\left|Z_{\mathrm{rt}}\left(N\right)\right|}^{p-1}\mathrm{sign}\left(Z_{\mathrm{rt}}\left(N\right)\right)Y_r^{*}\left(N\right)$ (10)

$F_i(N+1)=F_i\left(N\right)+\mathrm{\μ}\left|E_{\mathrm{it}}\left(N\right)\right|$

$\·\mathrm{sign}\left(E_{\mathrm{it}}\left(N\right)\right)|Z_{\mathrm{it}}\left(N\right){|}^{p-1}\mathrm{sign}\left(Z_{\mathrm{it}}\left(N\right)\right)Y_i^{*}\left(N\right)$

Fractional lower-order statistics mould value transform frequency domain multimode blind balance method by fractional lower-order statistics is combined with MTFMMA, makes FLOSMTFMMA stablize under the partition noise condition at α and also can bring into play performance preferably.

F. a kind of fractional lower-order statistics mould of the present invention value transform wavelet frequency domain multimode blind balance method

Before signal enters the FLOSMTFMMA equalizer, after it is carried out orthogonal wavelet transformation, invented a kind of fractional lower-order statistics mould value transform wavelet frequency domain multimode blind balance method WT-FLOSMTFMMA.Its principle, as shown in Figure 1.In Fig. 1, a (n) is for transmitting, and c (n) is the impulse response vector of channel, and c (n)=[c (n) ..., c (n-M+1)] ^T(subscript T represents transposition, and M represents channel length), b (n) is the signal vector through channel output, and w (n) is that α stablizes partition noise, and y (n) is through channel and the signal vector after being mixed with noise, v _r(n) and v _i(n) be respectively the real part y of y (n) _r(n) with imaginary part y _i(n) through signal vector corresponding after orthogonal wavelet transformation, R _r(N) and R _i(N) be respectively v _r(n) and v _i(n) through the signal vector after fast Fourier transform, Z _r(N) and Z _i(N) be the frequency-domain equalizer output signal, z _r(n) and z _i(n) be respectively Z _r(N) and Z _i(N) through the signal after Fast Fourier Transform Inverse, z _rt(n) and z _it(n) be the signal vector z after process mould value transform _t(n) real part and imaginary part, e _rt(n) and e _it(n) be real part and imaginary part through the time domain error function after the mould value transform, E _rt(N) and E _it(N) be respectively e _rt(n) and e _it(n) through real part and the imaginary part of the error function E (N) after Fourier transform, z (n) is the time-domain equalizer output signal that merges output finally by crossing.As shown in Figure 1

y(n)=c ^T(n)a(n)+w(n) (11)

v _r(n)=Qy _r(n)，v _i(n)=Qy _i(n) (12)

$e_{\mathrm{rt}}\left(n\right)=R_{\mathrm{rt}}^{\left(p\right)}-{\left|z_{\mathrm{rt}}\left(n\right)\right|}^p,$ $e_{\mathrm{it}}\left(n\right)=R_{\mathrm{it}}^{\left(p\right)}-{\left|z_{\mathrm{it}}\left(n\right)\right|}^p---\left(13\right)$

In formula, Q is the orthogonal wavelet transformation matrix, and the wavelet frequency domain equalizer is output as

Z _r(N)=R _r(N)F _r(N)，Z _i(N)=R _i(N)F _i(N) (14)

At this moment, the weight vector iterative formula of WT-FLOSMTFMMA is

$F_r(N+1)=F_r\left(N\right)+\mathrm{\μ}{\hat{R}}^{-1}\left(N\right)\left|E_{\mathrm{rt}}\left(N\right)\right|$

$\·\mathrm{sign}\left(E_{\mathrm{rt}}\left(N\right)\right){\left|Z_{\mathrm{rt}}\left(N\right)\right|}^{p-1}\mathrm{sign}\left(Z_{\mathrm{rt}}\left(N\right)\right)R_r^{*}\left(N\right)$ (15)

$F_i(N+1)=F_i\left(N\right)+\mathrm{\μ}{\hat{R}}^{-1}\left(N\right)\left|E_{\mathrm{it}}\left(N\right)\right|$

$\·\mathrm{sign}\left(E_{\mathrm{it}}\left(N\right)\right)|Z_{\mathrm{it}}\left(N\right){|}^{p-1}\mathrm{sign}\left(Z_{\mathrm{it}}\left(N\right)\right)R_i^{*}\left(N\right)$

In formula,

With

The real part R of expression frequency-domain equalizer input signal R (N) _r(N) with imaginary part R _i(N) conjugation,

For

Fast Fourier transform, and

The formula that obtains be

${\hat{R}}^{-1}\left(n\right)=\mathrm{diag}[{\mathrm{\σ}}_{j,0}^2\left(n\right),{\mathrm{\σ}}_{j,1}^2\left(n\right),\·\·\·,{\mathrm{\σ}}_{j,k}^2\left(n\right),{\mathrm{\σ}}_{j,k}^2\left(n\right),{\mathrm{\σ}}_{J+\mathrm{1,0}}^2\left(n\right),\·\·\·,{\mathrm{\σ}}_{J+1,k_J-1}^2\left(n\right)]$

Wherein, diag[] the expression diagonal matrix, With

Represent u respectively _{J, k}(n) with

Average power estimate, can be obtained by the following formula recursion

${\mathrm{\σ}}_{j,m}^2(n+1)={\mathrm{\β}}_{\mathrm{\σ}}{\mathrm{\σ}}_{j,m}^2\left(n\right)+(1-{\mathrm{\β}}_{\mathrm{\σ}})|u_{j,m}\left(n\right){|}^2$ (16)

${\mathrm{\σ}}_{J+1,m}^2(n+1)={\mathrm{\β}}_{\mathrm{\σ}}{\mathrm{\σ}}_{J+1,m}^2\left(n\right)+(1-{\mathrm{\β}}_{\mathrm{\σ}})|s_{J,m}\left(n\right){|}^2$

In formula, u _{J, m}(n) be that scale parameter is j, translation parameters is the wavelet conversion coefficient of m, s _{J, m}(n) for scale parameter is J, translation parameters is the change of scale coefficient of m, and j is scale parameter, and m ∈ Z is translation parameters, and J is the out to out of wavelet decomposition, and k is the translation parameters of corresponding wavelet function under scale parameter j, k _JBe the maximal translation of wavelet function under yardstick J, β _σSmoothing factor, and 0＜β _σ＜1.

Through after orthogonal wavelet transformation, the autocorrelation matrix of signal is more near diagonal matrix, and this moment, signal energy mainly concentrated near diagonal, and namely the correlation of signal has diminished.Therefore, the inventive method WT-FLOSMTFMMA has fast convergence rate, characteristics that mean square error is little, and performance is improved.

Embodiment

In order to verify the validity of the inventive method WT-FLOSMTFMMA, with FLOSFCMA and FLOSMTFMMA method object as a comparison, test.In experiment, the step-length of FLOSFCMA, FLOSMTFMMA and WT-FLOSMTFMMA is respectively 0.0002,0.0002,0.004, adopt the Db2 small echo to decompose, decomposition level is two-layer, small echo power initial value is 4, channel impulse response vector c=[0.9656,-0.0906,0.0578,0.2368], the equalizer tap number is 16, it is 1 that FLOSMTFMMA and WT-FLOSMTFMMA all adopt the 12nd tap initialization, it is 1 that FLOSFCMA adopts the 8th tap initialization, and broad sense signal to noise ratio (generalized signal-noise-ratio, GSNR) is 25dB.Stablize in partition noise at α, when the p=0.8499 in WT-FLOSMTFMMA and FLOSMTFMMA, 700 Monte-Carlo Simulation results as shown in Figure 7; When the p=0.63 in WT-FLOSMTFMMA and the p=0.6 in FLOSMTFMMA, 700 Monte-Carlo Simulation results as shown in Figure 8.

Fig. 7 (a) shows, the convergence rate of the inventive method WT-FLOSMTFMMA is than FLOSFCMA and fast approximately 3000 steps of FLOSMTFMMA, and the steady-state error of the inventive method WT-FLOSMTFMMA reduces approximately 2dB than FLOSFCMA.Fig. 8 (a) shows that the convergence rate of the inventive method WT-FLOSMTFMMA is than fast approximately 2500 steps of FLOSMTFMMA.

It is identical that Fig. 7 (b) ~ (d) and Fig. 8 (b) ~ (d) show that the inventive method WT-FLOSMTFMMA and the eye pattern of FLOSMTFMMA open effect, but all the eye pattern of ratio method FLOSFCMA to open effect clear.

By Fig. 7 and Fig. 8 as can be known, stablize in partition noise at α, the adaptive capacity of the inventive method WT-FLOSMTFMMA is the strongest.

Claims (2)

1. a fractional lower-order statistics mould value transform wavelet frequency domain multimode blind balance method, is characterized in that, comprises the steps:

Steps A, a (n) that will transmit obtains channel output vector b (n) through impulse response channel c (n), and wherein n is time series;

Step B adopts α to stablize partition noise w (n) and the described channel output vector of steps A b (n) obtains the front equalizer input signal y (n) of orthogonal wavelet transformation: y (n)=w (n)+b (n);

Step C gets its real part y to the described equalizer input signal y of step B (n) _r(n) and imaginary part y _i(n), then to real part y _r(n) and imaginary part y _i(n) carry out respectively orthogonal wavelet transformation, through the signal after orthogonal wavelet transformation be

v _r(n)=Qy _r(n)，v _i(n)=Qy _i(n)

In formula, Q is the orthogonal wavelet transformation matrix, v _r(n) and v _i(n) be respectively the real part y of time-domain equalizer input signal y (n) _r(n) and imaginary part y _i(n) through the signal component after orthogonal wavelet transformation, the real part Z of frequency-domain equalizer output Z (N) _r(N) and imaginary part Z _i(N) be respectively

Z _r(N)=R _r(N)F _r(N)，Z _i(N)=R _i(N)F _i(N)

In formula, N represents that length is the piece number of the data block of L, and L is equalizer weight vector length, F _r(N) and F _i(N) be respectively real part and the imaginary part of frequency-domain equalizer weight vector F (N), R _r(N) and R _i(N) be respectively v _r(n) and v _i(n) through frequency domain real part and imaginary part after fast Fourier transform;

Step D is to the real part Z of step C frequency-domain equalizer output signal Z (N) _r(N) and imaginary part Z _i(N) obtain respectively the real part z of time-domain equalizer output signal z (n) as Fourier inversion _r(n) and imaginary part z _i(n).

2. a kind of fractional lower-order statistics mould value transform wavelet frequency domain multimode blind balance method according to claim 1, is characterized in that, in described step C, the calculation procedure of frequency-domain equalizer weight vector F (N) is as follows:

Step C-1 calculates mould value transform time domain error function e _t(n) real part e _rt(n) with imaginary part e _it(n), computing formula is as follows:

$e_{\mathrm{rt}}\left(n\right)=R_{\mathrm{rt}}^{\left(p\right)}-|z_{\mathrm{rt}}\left(n\right){|}^p,$ $e_{\mathrm{it}}\left(n\right)=R_{\mathrm{it}}^{\left(p\right)}-|z_{\mathrm{it}}\left(n\right){|}^p$

$R_{\mathrm{rt}}^{\left(p\right)}=\frac{E\left\{\right|a_{\mathrm{rt}}\left(n\right){|}^{2p}\}}{E\left\{\right|a_{\mathrm{rt}}\left(n\right){|}^p\}},$ $R_{\mathrm{it}}^{\left(p\right)}=\frac{E\left\{\right|a_{\mathrm{it}}\left(n\right){|}^{2p}\}}{E\left\{\right|a_{\mathrm{it}}\left(n\right){|}^p\}}$

In formula, || be modulo operation, p be greater than zero less than 1 positive number, E{} represents to ask mathematic expectaion, a _rt(n) and a _it(n) be respectively the real part a of a that transmits (n) _r(n) with imaginary part a _i(n) pass through respectively signal component after the mould value transform,

With

Be respectively a _rt(n) and a _it(n) p rank statistics mould value, z _rt(n) and z _it(n) be respectively the real part z of time-domain equalizer output signal z (n) _r(n) with imaginary part z _i(n) through real part and imaginary part after the mould value transform; Step C-2 is to mould value transform time domain error function e _t(n) real part e _rt(n) with imaginary part e _it(n) make Fourier transform after, obtain mould value transform error of frequency domain function E _t(N) real part E _rt(N) with imaginary part E _it(N);

Step C-3 calculates frequency-domain equalizer weight vector F (N), and the formula of its iterative process is:

$F_r(N+1)=F_r\left(N\right)+\mathrm{\μ}{\hat{R}}^{-1}\left(N\right)\left|E_{\mathrm{rt}}\left(N\right)\right|$

$\·\mathrm{sign}\left(E_{\mathrm{rt}}\left(N\right)\right)|Z_{\mathrm{rt}}\left(N\right){|}^{p-1}\mathrm{sign}\left(Z_{\mathrm{rt}}\left(N\right)\right)R_r^{*}\left(N\right)$

$F_i(N+1)=F_i\left(N\right)+\mathrm{\μ}{\hat{R}}^{-1}\left(N\right)\left|E_{\mathrm{it}}\left(N\right)\right|$

$\·\mathrm{sign}\left(E_{\mathrm{it}}\left(N\right)\right)|Z_{\mathrm{it}}\left(N\right){|}^{p-1}\mathrm{sign}\left(Z_{\mathrm{it}}\left(N\right)\right)R_i^{*}\left(N\right)$

In formula, μ is iteration step length, and symbolic operation, Z are got in sign () expression _rt(N) and Z _it(N) be respectively through the frequency-domain equalizer output signal Z after the mould value transform _t(N) real part and imaginary part; With The real part R of expression frequency-domain equalizer input signal R (N) _r(N) with imaginary part R _i(N) conjugation;

For

Fast Fourier transform, and

The formula that obtains be

${\hat{R}}^{-1}\left(n\right)=\mathrm{diag}[{\mathrm{\σ}}_{j,0}^2\left(n\right),{\mathrm{\σ}}_{j,1}^2\left(n\right),\·\·\·,{\mathrm{\σ}}_{j,k}^2\left(n\right),{\mathrm{\σ}}_{J+\mathrm{1,0}}^2\left(n\right),\·\·\·,{\mathrm{\σ}}_{J+1,k_J-1}^2\left(n\right)]$

Wherein, diag[] the expression diagonal matrix,

With

Represent u respectively _{J, k}(n) with

Average power estimate, can be obtained by the following formula recursion:

${\mathrm{\σ}}_{j,m}^2(n+1)={\mathrm{\β}}_{\mathrm{\σ}}{\mathrm{\σ}}_{j,m}^2\left(n\right)+(1-{\mathrm{\β}}_{\mathrm{\σ}})|u_{j,m}\left(n\right){|}^2$

${\mathrm{\σ}}_{J+1,m}^2(n+1)={\mathrm{\β}}_{\mathrm{\σ}}{\mathrm{\σ}}_{J+1,m}^2\left(n\right)+(1-{\mathrm{\β}}_{\mathrm{\σ}})|s_{J,m}\left(n\right){|}^2$

In formula, u _{J, m}(n) be that scale parameter is that j, translation parameters are the wavelet conversion coefficient of m, s _{J, m}(n) for scale parameter is that J, translation parameters are the change of scale coefficient of m, J is the out to out of wavelet decomposition, and k is the translation parameters of corresponding wavelet function under scale parameter j, k _JThe expression out to out is the maximal translation of wavelet function under J, β _σSmoothing factor, and 0＜β _σ＜1.

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